Quixotic traveller cut short horseplay (8)
I believe the answer is:
romantic
'quixotic' is the definition.
(I know that quixotic can be written as romantic)
'traveller cut short horseplay' is the wordplay.
'traveller' becomes 'roma' (as in Romani Travellers).
'cut short' means to remove the last letter.
'horseplay' becomes 'antic' (both can mean silly behaviour).
'roma' with its last letter removed is 'rom'.
'rom'+'antic'='ROMANTIC'
(Other definitions for romantic that I've seen before include "Coin mart (anag.)" , "Evoking love; post-Classical" , "Sentimental" , "Involving a love affair, appealing to the tender emotions" , "Amorous, showing loving feeling" .)