Motorbike carriage was competitive, and is on the up (7)
I believe the answer is:
sidecar
'motorbike carriage' is the definition.
'sidecar' can be an answer for 'carriage' (thesaurus). I'm not certain of the 'motorbike' bit.
'competitive and is on the up' is the wordplay.
'competitive' becomes 'raced' (I can't justify this - if you can you should give a lot more credence to this answer).
'and' says to put letters next to each other.
'on the up' is a reversal indicator (in a down clue, letters go up).
'raced'+'is'='racedis'
'racedis' in reverse letter order is 'SIDECAR'.
'was' is the link.
Can you help me to learn more?
(Other definitions for sidecar that I've seen before include "Cocktail; bike attachment" , "In which Gromit goes" , "Attachment to motorcycle to accommodate passenger" , "Attachment on motorcycle to carry passenger" , "Attachment to motor cycle" .)