Cut the new bandages carefully at first (4)
I believe the answer is:
etch
'cut' is the definition.
(I've seen this in another clue)
'the new bandages carefully at first' is the wordplay.
'new' indicates an anagram.
'bandages' indicates putting letters inside.
'at first' says to take the initial letters.
The first letter of 'carefully' is 'c'.
'the' with letters rearranged gives 'eth'.
'eth' placed around 'c' is 'ETCH'.
(Other definitions for etch that I've seen before include "Make picture by engraving metal" , "Cut using sharp instrument" , "Score deeply" , "Engrave; fix firmly" , "Carve into surface, impress deeply" .)