Pet shows anxiety when on a ship (6)
I believe the answer is:
caress
'pet' is the definition.
(I know that pet is a more specific form of the action caress)
'anxiety when on a ship' is the wordplay.
'anxiety' becomes 'care' (care is a kind of anxiety).
'when on' says to put letters next to each other.
'a ship' becomes 'SS' (prefix in ship names eg SS Great Britain).
'care'+'ss'='CARESS'
'shows' acts as a link.
(Other definitions for caress that I've seen before include "show of affection" , "Pat" , "Stroke lovingly" , "Scares into handle lovingly" , "pet[s]" .)