This post is a part of a series on Providing Seamless Transitions Between Songs in Your Worship Set, Please begin with the first article as these build upon one another.
Take a look at this short explainer video:
Note: It is generally best to move up in keys, not down.
It is almost always best to end one song and immediately start the next introduction in the higher key. SHORT GAP

Example 1:
Forever (in G) – How Great Is Our God (in A)
We end, Forever, and after a brief stop, the intro begins for How Great Is Our God.
Long Version
Short Version
Example 2:
How Great Is Our God (in B flat) – Holy Holy Holy (in C)
The band plays the full outro of How Great Is Our God, has a brief pause, followed by quarter notes in the new key leading into the first verse of Holy Holy Holy.
Long Version
Short Version
At times, using the dominant seventh chord of the second song is effective to lead you to the new key. Example: B-flat-F/G (IV/V in new key) – G7 (V7 in new key) – C NO GAP
While just having a short gap between the two works nicely, you can experiment with a chord progression such as this one to tastefully move to the new key.
Modulate inside the first song to sing a verse, chorus, or bridge a half or whole step higher (to the same key as the second song), then use one of the methods for joining songs in the same key.
If you are singing a song in the key of G and want to transition to a song in A, then perhaps sing the final chorus of the first song in G and then transition as you would for two songs in the same key. Be sure your modulation does not place the singing range too high in the first song.