To try to keep up with vessel, galley periodically used (6)
I believe the answer is:
juggle
'to try to keep up' is the definition.
(juggling is keeping items up in the air)
'with vessel galley periodically used' is the wordplay.
'with' says to put letters next to each other.
'vessel' becomes 'jug' (jug is a kind of vessel).
'periodically used' indicates alternate letters (letters selected regularly or periodically).
The alternate letters of 'galley' are 'gle'.
'jug' put next to 'gle' is 'JUGGLE'.
(Other definitions for juggle that I've seen before include "Keep several things going at the same time" , "Toss and catch a number of things at once" , "Keep things in the air" , "Manipulate objects with great dexterity" , "Keep several objects in the air at once" .)