Female carrying oxygen pump, say (4)
I believe the answer is:
shoe
'pump say' is the definition.
(pump is a kind of shoe)
'female carrying oxygen' is the wordplay.
'female' becomes 'she' (I've seen this before**).
'carrying' means one lot of letters goes inside another.
'oxygen' becomes 'o' (atomic symbol for oxygen).
'she' placed around 'o' is 'SHOE'.
(Other definitions for shoe that I've seen before include "Sandal or brogue?" , "Footwear - playing-card dispenser - part of a brake" , "Brogue, for example" , "What one needs for a horse" , "Plate on horse" .)