Notice period buyout - head of department refusing to relieve

Need some clarity on notice period buyout. As per the appointment it's mentioned we can either serve 90days of Np or buyout. But the concern is now the head of department refusing to relieve and instead asking to serve full 90days of notice period.
Resource got offer and accepted to join the.new organisation within 45days thinking he can buyout the notice period but in the current organization they.seems to be threatening. Can some one pls out with a suggestion

If there is a specific stipulation that the employee can resort to buy out in stead of serving the entire notice period, the employer can not simply reject it unless there are unavoidable/extenuating circumstances like pendency of a time-bound assignment in which the employee has got an important role that can not be substituted.