Life after S21

Other

I have issued a S21 to a tenant. However; now I have decided to let them stay for a while and I know it has become a periodic tenancy. My question is now that a valid S21 has been served, when will it expire. If I increase the rent will it invalidate the S21?. Will I have to reissue a S21 in order to get possession? Its a long standing tenant, nearly 10 years and the property has been given below market value which is one reason why he does not want to leave. the other reason is because he does not want to divulge his credentials eg did not permit me to get credit reference, did not provide date of birth, et etc. I gave the property based on a letter from his employer and I knew he had money coming in and that if he did a runner I knew where to find him etc. the problem is now he does not want to move out and as he has been there long will be difficult to get him out.
Rainbow