Finally including me in relative increase (7)
I believe the answer is:
augment
'increase' is the definition.
(augmenting is a kind of increasing)
'finally including me in relative' is the wordplay.
'finally' indicates one should take the final letters.
'in' indicates putting letters inside.
'relative' becomes 'aunt' (aunt is a kind of relative**).
The last letter of 'including' is 'g'.
'g'+'me'='gme'
'gme' put within 'aunt' is 'AUGMENT'.
(Other definitions for augment that I've seen before include "Supplement" , "Add to, increase" , "Grow - intensify" , "Expand" , "get longer" .)