Moved to a new city – how to start academically networking?
Contact the schools doing relevant work and ask to be added to their seminar notification lists. Attend the seminars and participate in discussion afterwards. You needn't mention your affiliation.
Contact the people doing relevant work and offer to present a seminar yourself (if your employer will allow it). Most university schools run seminar series and are always on the lookout for new speakers, especially external speakers. List the affiliation you had when you did the research about which you will be speaking. When they accept your seminar offer, ask if they would also mind scheduling you some time on the same day to speak one-on-one with people working in your field.
If you are in an applied field, look into whether there is an active professional society group in your field in the new city. Join it and attend their events. If there there is no active group, consider starting one: if you are willing to do the leg-work involved in organising a few good seminars, professional networking dinners, entertaining debates or other activities, people will join.