Phil's number one cut — that was close! (4)
I believe the answer is:
phew
'was close' is the definition.
I can't judge whether this definition defines the answer.
'phil's number one cut' is the wordplay.
'phil's number one' becomes 'p' (hst letter of 'phil').
'cut' becomes 'hew' (I've seen this before).
'p'+'hew'='PHEW'
'that' is the link.
Can you help me to learn more?
(Other definitions for phew that I've seen before include "Exclamation of relief" , "Recover unharmed" , "Sound relieved" , "What a relief! It's hot!" , "Gosh, that's a relief!" .)