Barely enough, with no time for examination (4)
I believe the answer is:
scan
'examination' is the definition.
(scan is a kind of examination)
'barely enough with no time' is the wordplay.
'barely enough' becomes 'scant' (scant means barely enough or barely sufficient).
'with no' is a deletion indicator.
'time' becomes 't' (abbreviation).
'scant' with 't' removed is 'SCAN'.
'for' is the link.
(Other definitions for scan that I've seen before include "Browse or skin over, say book" , "Study the metre" , "show in this?" , "Medical procedure" , "Read electronically" .)