It goes up with the start of my self-love (7)
I believe the answer is:
egotism
'self-love' is the definition.
(I've seen this before)
'it goes up with the start of my' is the wordplay.
'up with' indicates anagramming the letters.
'the start of' means to remove the last letter.
'my' with its last letter removed is 'm'.
'it'+'goes'='itgoes'
'itgoes' with its letters anagrammed with 'm' can make 'EGOTISM'.
(Other definitions for egotism that I've seen before include "Excessive absorbtion in oneself" , "Self-love" , "Excessive conceit" , "Selfishness" , "Self-obsession" .)