Take home sailors after first eyeing airmen (4)
I believe the answer is:
earn
'take home' is the definition.
(as in taking home money)
'sailors after first eyeing airmen' is the wordplay.
'sailors' becomes 'RN' (abbreviation for Royal Navy).
'after' means one lot of letters go next to another.
'first' says to take the initial letters.
The first letters of 'eyeing airmen' is 'ea'.
'rn' put after 'ea' is 'EARN'.
(Other definitions for earn that I've seen before include "Deserve; get paid" , "Gain by working" , "Attain" , "Warrant" , "Be paid for work" .)