The mobile service provider will have the location of the phone with reference to the mobile signal tower to which it gets linked. However if the phone is active with data on and has the GPS facilities linked to Facebook account etc. and on and open, then the locations would have got recorded in such account logs automatically. That would help to trace the approximate location or movement path.
these information will not be easily divulged by the service operators . They may need solid justification from the police or aw enforcing authorities, from the duly authorised official. Mostly these take some time and procedure, unless the case is very sensational and got high media attention. Even then getting information from Facebook etc. is difficult. But Local mobile operators may oblige better to the police.
The police can trace the person who is using the phone and SIM in case that is stolen, and still in use.
While posting this, I also offer and convey my prayers for the safe return of the missing person.
Please co-operate and liaise with the police as well as doing your own enquiries to all those who would have contacts and communication with your sister.