Moved to a new city – how to start academically networking? I have recently moved away from the town and university where I completed my masters degree to another city for personal reasons. Now I work here in academic information services and part of my work is research.

However, I would like to put a stronger focus on research and concept-level work rather than doing tasks in technical services. To achieve this, I feel I need to do more academic networking outside of work which is quite difficult as my employing institution does not like being mentioned as affiliation in professional networking. 

The problem is: How to (re-)start academic networking when I don't really have an institutional or project affiliation?

I know this can be seen as a workplace-related question, but I am specifically interested in academic networking - participate in research discussion groups, maybe get to teach a small Bachelor course related to my work, possibly find a partner for collaboration on a paper... The city I now live in has some universities, but there does not seem to be any connection to the university or institute I graduated in.

I really feel stuck in this situation. Any suggestion on this would be welcome!
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.