Which course in arboriculture are you planning on doing?? ( what is the recognised qualification you will obtain?? )
Mandatory training and tickets you will need will be nptc or lantra equivilent. Cs30 + cs31, chainsaw maintenance, felling of small trees and cross cutting.
You will need the above before any firm would consider employing you or an insurer will insure.
To climb you will need cs38, using a rope and harness and carrying out aeriel rescue.
Plus cs39, using a chainsaw in a tree.
Your college course will include cs30 + 31 but anything else will be optional. You maybe of