Reconstitution of Partnership Firm on Death of a Partner

Hello all.
As per Section 42(c) of Indian Partnership Act, 1932: Subject to contact between the partners, a firm is dissolved by the death of a partner.

Further, as per section 39: The dissolution of a partnership between all the partners of a firm is called the "dissolution of the firm".

So, in case when one of the partners of a partnership firm expires, is it sufficient for a firm to legally carry on its business by making a new partnership deed with admission of a new partner; while continuing the old firm (I.e. Firm will survive and it's registration details like PAN, GST, Trade License shall remain same).

Essentially, the question here I think is, that, is there any difference between "Reconstitution of Partnership" and "Reconstitution of Partnership Firm"?