Madly repeat about last letter of a swing (7)
I believe the answer is:
trapeze
'a swing' is the definition.
(I know that trapeze is a type of swing)
'madly repeat about last letter' is the wordplay.
'madly' is an anagram indicator.
'about' means one lot of letters goes inside another.
'last letter' becomes 'Z' (last letter of the alphabet).
'repeat' with letters rearranged gives 'trapee'.
'trapee' going around 'z' is 'TRAPEZE'.
'of' acts as a link.
(Other definitions for trapeze that I've seen before include "Flying circus apparatus?" , "What the daring young man in the circus flies on" , "Horizontal bar as swing for acrobats" , "Circus attraction" , "Swing used by circus acrobats" .)