Is there any specific deadline by which existing laws need to be brought into conformity with the constitution as per this section?
No, there is no specific deadline by which existing laws need to be brought into conformity with the constitution as per this section. It states that "any law in force immediately before the commencement of this Constitution in the territory of India with respect to any of the matters referred to in sub-clause (i) of clause (a) or providing for punishment for any act referred to in sub-clause (ii) of that clause shall, subject to the terms thereof and to any adaptations and modifications that may be made therein under article 372, continue in force until altered or repealed or amended by Parliament."