International travel during a job switch

Currently on a work (Engineer/Humanities/Int'l) Visa with 2+ years left. Switching Jobs on a tight timeline.

New job requires international travel immediately after joining from day 1. New job is fine with me booking flights earlier also, so thinking of using all my remaining paid leaves from old job at the end and doing a small personal vacation just before starting work at the new job.

Any possible issues with visa/tax/pension etc. I should be worried about?

Thanks in advance