what does it mean?
when we say : Rebels have tightened their grip on the city
1- Rebels have occupied the city and have taken the control of the city
or
2- Rebels have surrounded the city and they are trying to occupy the city

Question

what does it mean?
when we say : Rebels have tightened their grip on the city
 1- Rebels have occupied the city and have taken the control of the city
or
2- Rebels have surrounded the city and they are trying to occupy the city

Answer

It sounds more like the first to me. If it were the second, I think 'Rebels are trying to tighten their grip on the city' would be more appropriate.