You can always apply for other Government jobs. The exact procedure for applying is indicated below:-
(a) Whenever there is any new vacancy, send an application like other candidates. But please indicate in the application about your present employment. Please don't conceal any information.
(b) Before sending the application, please keep a copy of the same.
(c) Then intimate your present office about applying for anotherGovernment job and request your office to forward the application through proper channel.
(d) If the application is forwarded by your office, then it is perfectly alright. If not, even then you don't have any problem. There is a provision in the rule that if it is specifically not mentioned that your request has been turned down, it automatically implies that your intimation has been taken on record. In that case, you would not face any problem in case of your subsequent selection.
(e) I personally left three Government jobs and ultimately settled in the fourth one. I had no problem. Nowadays, I a forward the application of my subordinates as Head of Office. Only remember that you should not conceal any information and you should formally intimate your present office. Intimating your present office has many other advantages, which you will know in due course.
Caution: Explosive. Handle with care.