Do press on, struggling in such a walk? (9)
I believe the answer is:
sponsored
'such a walk?' is the definition.
(as in a sponsored walk)
'do press on struggling' is the wordplay.
'struggling' is an anagram indicator (the letters struggle or wriggle into a new form).
'do'+'press'+'on'='dopresson'
'dopresson' anagrammed gives 'SPONSORED'.
'in' is the link.
(Other definitions for sponsored that I've seen before include "With backing" , "(Of event) supported financially" .)