to tighten one's grip on something

[Sammy Sam]

Is it ok to say

They have tightened their grip on the market share.

And can we use the same expression in this way?

The police has tightened its grip on the gangsters

 

[emsr2d2]

Is it ok OK/okay to say "They have tightened their grip on the market share no full stop here" and can we use the same expression in this the following way?

The police has tightened its grip on the gangsters.

Note my changes above.
Both sentences are possible.

 

[Piscean]

The police has tightened its grip on the gangsters.

The police have tightened their grip on the gangsters.