Home, having had a puncture (4)
I believe the answer is:
flat
'a puncture' is the definition.
(I've seen this before)
'home having' is the wordplay.
I cannot quite see how this works, but
'home' could be 'at' (synonyms) and 'at' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
'had' acts as a link.
Can you help me to learn more?
(Other definitions for flat that I've seen before include "Personal residence" , "Featureless" , "razed to the ground, having had blow-out" , "Pied-a-terre" , "Not sloping; apartment" .)