I travel into place to have a hearty meal (3,3)
I believe the answer is:
pig out
'have a hearty meal' is the definition.
(to pig out is to devour food)
'i travel into place' is the wordplay.
'travel' becomes 'go' (synonyms).
'into' indicates putting letters inside.
'place' becomes 'put' (synonyms).
'i'+'go'='igo'
'igo' going inside 'put' is 'PIG OUT'.
'to' is the link.
(Other definitions for pig out that I've seen before include "overindulge" , "Eat too much food" , "gorge" , "go on a binge" , "feast" .)