Quickly, by arrangement, train on the rink (2,1,5)
I believe the answer is:
in a trice
'quickly' is the definition.
(I've seen this before)
'arrangement train on the rink' is the wordplay.
'arrangement' indicates anagramming the letters.
'on' means one lot of letters goes inside another.
'the rink' becomes 'ice' (ice rink is a kind of rink).
'train' with letters rearranged gives 'natri'.
'natri' going inside 'ice' is 'IN A TRICE'.
'by' is the link.
(Other definitions for in a trice that I've seen before include "quickly" , "Pronto" .)