Changed job to a different city but still using work and residence permits from old city

Hello,
I was previous working in Tianjin but found a new job and moved to Beijing though still living in Tianjin. I was issued a release letter from my previous employee. However, I have worked for almost 2 months with the new company still using my work and residence permits issued at Tianjin. I am now going to apply for the transfer of my work and residence permits to Beijing. Would there be any sanctions? Considering the fact that I have worked for 2 months without applying for the transfer? Also, I still live in Tianjin and might move to Beijing later on. Can I apply for residence permit in Beijing using my rent contract from Tianjin?
Thanks.