newReharmonisation means changing the chords of a song, for example when you are making an arrangement. It is quite common in jazz and far less common in pop music. A lot of reharmonisation techniques will result in a jazzy sound.

In reharmonizing you have an enormous range of possibilities. If you have limited experience in this field, you might be overwhelmed by that. Therefore, I have made a list of techniques you might use to find new chords. The techniques go from rather easy to increasingly complex.

All examples below are based on the following chords:
|   C   |   F   |   DM   |   G7   |   C   |

Technique 1. Put additions in the chords

Enrich the chords by adding notes to the triads, for example a seventh or a ninth:
|   C9  |   F^  |   DM7   |   G7   |   C   |
You might also create harmonies with five notes:
|   C^9  |   F96  |   DM79  |   G76  |   C96  |
Especially in the dominant seventh chord a lot of extensions are possible. Instead of a ninth you might choose a <9, <10 of >11:
|   C   |   F   |   DM   |   G7<9  |   C   |

Technique 2. Change the third or fifth of the chord

Instead of adding notes to the harmonies, you might move the notes of the triad. For example, change the third into an sus4:
|   C   |   F   |   DM   |   G7sus4  |   C   |
You might change the fifth to a flat fifth:
|   C   |   F   |   DM<5  |   G7   |   C   |
Or you might change it to a sharp fifth:
|   C   |   F   |   DM   |   G7>5  |   C   |

Technique 3. Put in a chord that leads to an existing chord

In these chords F is sounding before DM, though this chord does not really ‘lead’ to DM, according to the circle of fifth. However, the chord AM does lead to DM. Therefore, it might be a good option to replace the F by AM:
|   C   |   AM   |   DM   |   G7   |   C   |
Another option is to replace F by A7, because that chords leads to DM as well:
|   C   |   A7   |   DM   |   G7   |   C   |
In the same manner, you might replace DM with D7, because it leads to G:
|   C   |   F   |   D7   |   G7   |   C   |
Another way to describe this technique is: go back one step in the circle of fifth, starting from one of the existing chords.

Technique 4. Put in a chord that follows from an existing chord

Like mentioned above, F is before DM, though it doesn’t lead to that harmony. A chord that you might expect after F is B@. Thus, you might replace DM by B@:
|   C   |   F   |   B@  |   G7   |   C   |
Another way to describe this technique is: go on one step in the circle of fifth, starting from one of the existing chords.

Technique 5. Replace an existing chord by two chords

Instead of replace a chord by another one, you might insert a chord. You might make up the inserted chord with one of the techniques mentioned above. Inserting a chord creates a lot of possibilities. Here are some ideas.

You might replace C by C and C7, because the latter harmony leads to F:
|   C   C7   |   F   |   DM   |   G7   |   C   |
You might replace C by Csus4 en C, because Csus4 resolves to C:
|   Csus4   C   |   F   |   DM   |   G7   |   C   |
If you do the above, it will sound nice if you do the same on F, creating some symmetry in the harmonies:
|   Csus4   C   |   Fsus4 F   |   DM   |   G7   |   C   |
A chord that leads to C as well is GM. Therefore you might replace C by GM en C. A minor chord GM will sound more interesting than a major chord G, because then the chords are the scale degrees II and V for F:
|   GM   C   |   F   |   DM   |   G7   |   C   |
You might replace F by F en B@, because the former leads to the latter in the circle of fifth:
|   C   |   F   B@   |   DM   |   G7   |   C   |
You might replace DM by AM and DM, because AM leads to DM:
|   C   |   F   |   AM   DM   |   G7   |   C   |
Or you might replace DM by A7 and DM:
|   C   |   F   |   A7   DM   |   G7   |   C   |
In the same manner, you might replace G7 by D7 and G7:
|   C   |   F   |   DM   |   D7   G7   |   C   |
If you have already replaced DM by D7, you might replace G7 by DM7 and G7:
|   C   |   F   |   D7   |   DM   G7   |   C   |
An option that is used a lot is to replace the dominant chord on the scale degree V (G7 in this example) by a sus4 chord and its resolution:
|   C   |   F   |   DM   |   G7sus4   G7   |   C   |
Finally, the last chord C might be replaced in the same manner by a sus4 chord plus resolution:
|   C   |   F   |   DM   |   G7   |   Csus4   C   |

Split several chords

If you have split the chords on one spot, you might continue to do that, zo the harmonic speed will be constant. If you insert a dominant chord before each chord, we get the following harmonies:
|   C   C7   |   F   A7   |   DM   D7   |   G7   |   C   |
Using all these dominant chords, the harmonies get a real drive, creating a kind of bluesy feel.

Instead of dominant chords, you might insert harmonies that fit in the key:
|   C   C^  |   F   AM7   |   DM   DM7   |   G7   |   C   |
The atmosphere of these chords is definitely sweeter than the previous example.

Technique 6. Tritone substitution

Now we get to the difficult part. A tritone substitution is replace a dominant chord by (more or less) the same chord a tritone lower. (A tritone is a sharp fourth, literally it means three whole tones.)

You might replace G7 by a chord a tritone lower, that is D@7:
|   C   |   F   |   DM   |   D@7   |   C   |
Tritone substitutions sound good when there are sufficient jazzy extensions in the chords:
|   C^9  |   F796  |   DM79  |   D@79  |   C69  |

Combining techniques

All above techniques may be combined, of course. You might put and extensions to a chord (technique 1) and at the same to make it sus4 (technique 2):
|   C   |   F   |   DM   |   G79sus4  |   C   |
You might replace a chord (technique 3 or 4) and directly apply a tritone substitution (technique 6):
|   C   |   E@7   |   DM   |   G7   |   C   |
In the example above, we have replaced F by the dominant of DM, that is A7. Subsequently, we have applied tritone substitution on F, resulting in a E@7.

Think up harmonies that fit the melody

In all examples in the post, we didn’t take into account any melody. If you’re working on a real song, the chords you make up may be incompatible with the melody. In that case you have to look for other possibilities of course (or change the melody).