Antelope leaving delta shows style and vigour (4)
I believe the answer is:
elan
'style and vigour' is the definition.
(I've seen this before)
'antelope leaving delta' is the wordplay.
'antelope' becomes 'eland' (eland is a kind of antelope).
'leaving' is a deletion indicator.
'delta' becomes 'd' (phonetic alphabet: alpha, bravo, charlie etc.).
'eland' with 'd' removed is 'ELAN'.
'shows' is the link.
(Other definitions for elan that I've seen before include "spirit" , "Snap" , "French flair" , "Combination of style and vigour" , "Flair and dash" .)