Because defendant Welsbach Electric Corp., the named insured under the policy issued by Century, and the City, an additional insured under the policy, were adverse parties in the underlying action, the City had an independent obligation to provide timely written notice of the claim to Century (see Travelers Ins. Co. v Volmar Constr. Co., 300 AD2d 40, 44 [2002]). Further discovery as to whether Welsbach provided timely notice would serve no purpose (see American Mfrs. Mut. Ins. Co. v CMA Enters., 246 AD2d 373 [1998]).
Since Century asserted its late notice defense 92 days after receiving the City’s summons and complaint, its disclaimer cannot be held to be timely as a matter of law (see CPLR 3012 [c]; Insurance Law § 1212 [b]). While the City waived any defense based on lack of personal jurisdiction in the parties’ agreement *323extending Century’s time to answer, it did not waive its right to assert an untimely disclaimer defense (cf. DiGuglielmo v Travelers Prop. Cas., 6 AD3d 344, 346 [2004], lv denied 3 NY3d 608 [2004]).
Nor can Century’s notice of disclaimer be held to be untimely as a matter of law, since Century asserts that it needed time to investigate the 10-year-old claim. However, an issue of fact exists whether Century conducted its investigation promptly, diligently and in good faith (see Those Certain Underwriters at Lloyds, London v Gray, 49 AD3d 1, 7 [2007]; cf. 2540 Assoc. v Assicurazioni Generali, 271 AD2d 282, 284 [2000]). Contrary to Century’s contention, discovery as to its investigation would not violate the attorney-client and protected work-product privileges (see Brooklyn Union Gas Co. v American Home Assur. Co., 23 AD3d 190, 191 [2005]).
Contrary to Century’s further contention, Insurance Law § 3420 (d) protects the insured from the insurer’s unreasonable delays in disclaiming coverage even where, as here, the underlying claim has been satisfied (see e.g. 474431 Assoc. v AXA Global Risks US Ins. Co., 18 AD3d 604, 605 [2005]).
In light of our determination, we do not address Century’s remaining contentions. Concur—Tom, J.P., Buckley, Sweeny and Moskowitz, JJ. [See 11 Misc 3d 1085(A), 2006 NY Slip Op 50705(U).]