Pat gets support, coming first in swimming event (10)
I believe the answer is:
backstroke
'swimming event' is the definition.
'backstroke' can be an answer for 'swimming' (thesaurus). I am not certain of the 'event' bit.
'pat gets support coming first' is the wordplay.
'pat' becomes 'stroke'.
'gets support' becomes 'back' (I am not sure about this - if you are sure you should believe this answer much more).
'coming first' means one lot of letters go next to another.
'stroke' after 'back' is 'BACKSTROKE'.
'in' is the link.
Can you help me to learn more?
(Other definitions for backstroke that I've seen before include "Swimming style" , "Way to move through water looking upwards" , "action?" .)