Yes — you absolutely can train to become a driving instructor around your current job. In fact, many people do it this way. The DVSA qualification process is flexible, and most training providers offer part-time, evening, and weekend options to fit around work or other commitments.
Time needed: 2 – 4 weeks (part-time)
Time needed: 1 – 2 months part-time
Time needed: 2 – 6 months part-time