Mystic and I travel back on back of donkey (4)
I believe the answer is:
yogi
'mystic' is the definition.
(I've seen this before)
'i travel back on back of donkey' is the wordplay.
'travel' becomes 'go' (synonyms).
'back' says the letters should be written in reverse.
'on' is a charade indicator (letters next to each other).
'back of' suggests the final letters.
The last letter of 'donkey' is 'y'.
'i'+'go'='igo'
'igo' in reverse letter order is 'ogi'.
'ogi' put after 'y' is 'YOGI'.
'and' is the link.
(Other definitions for yogi that I've seen before include "Follower of a Hindu philosophy involving mind and body" , "Hindu teacher" , "Flexible figure" , "Practitioner of yoga" , "Cartoon bear; Hindu ascetic" .)