They may be inflated, for example, and very large (4)
I believe the answer is:
egos
'they may be inflated' is the definition.
(I've seen this in another clue)
'example and very large' is the wordplay.
'example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'and' means one lot of letters go next to another.
'very large' becomes 'os' (abbreviation for oversize).
'eg'+'os'='EGOS'
'for' is the link.
(Other definitions for egos that I've seen before include "feelings of self-importance" , "Self-images" , "People's personal pride - the parts of them that are conscious" , "Lots of self-esteem" .)