Object to being almost modest (5)
I believe the answer is:
demur
'object' is the definition.
(to demur is to object to something)
'almost modest' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'modest' becomes 'demure' (I've seen this before).
'demure' with its final letter removed is 'DEMUR'.
'to being' acts as a link.
(Other definitions for demur that I've seen before include "Politely disagree" , "Dissent, object" , "Raise scruples" , "Take exception (to)" , "Object gently" .)