Rump steak's prime cut to swallow (4)
I believe the answer is:
seat
'rump' is the definition.
(synonyms)
'to swallow' is the wordplay.
'to' becomes 's' (I can't justify this - if you can you should believe this answer much more).
'swallow' becomes 'eat' (I've seen this before).
's'+'eat'='SEAT'
'steak's prime cut' acts as a link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for seat that I've seen before include "Chair, bench, saddle, etc" , "Somewhere to sit" , "Settle in" , "Eg, chair, stool" , "Position (in parliament)" .)