Greet trouble with aspiration (4)
I believe the answer is:
hail
'greet' is the definition.
(I know that hail is a type of greet)
'trouble with aspiration' is the wordplay.
'trouble' becomes 'ail' (synonyms).
'with' means one lot of letters go next to another.
'aspiration' becomes 'h' (speech sound from a puff of breath).
'ail' put after 'h' is 'HAIL'.
(Other definitions for hail that I've seen before include "Greet; frozen rain" , "Greet - precipitation" , "Call for - praise, vociferously" , "Fall of ice" , "Greet - bad weather" .)