Increase is relative when false gem is inset (7)
I believe the answer is:
augment
'increase' is the definition.
(I know that augment is a more specific form of the action increase)
'relative when false gem is inset' is the wordplay.
'relative when' becomes 'aunt' (I can't explain this - if you can you should give a lot more credence to this answer).
'false' is an anagram indicator.
'is inset' means one lot of letters goes inside another (some letters are set inside others).
'gem' anagrammed gives 'gme'.
'aunt' placed around 'gme' is 'AUGMENT'.
'is' acts as a link.
Can you help me to learn more?
(Other definitions for augment that I've seen before include "Supplement" , "get longer" , "Grow - intensify" , "Expand" , "Enlarge or increase" .)