This clearly written Court of Appeals case lays out the Insurance carrier’s obligation to defend legal malpractice cases, and what happens when they refuse to defend.  K2 Inv. Group, LLC v American Guar. & Liab. Ins. Co. ,2013 NY Slip Op 04270 , Decided on June 11, 2013  Court of Appeals, Smith, J. tells us that when the carrier wrongfully fails to defend, it cannot then litigate other policy exclusions, and can (but not in this case) be responsible for bad faith amounts in excess of the policy.
 

"We affirm the summary judgment in plaintiffs’ favor on the breach of contract claims without reaching the question that divided the Appellate Division: the applicability of the insured’s status exclusion and the business enterprise exclusion to American Guarantee’s duty to indemnify Daniels for a judgment based on legal malpractice. We hold that, by breaching its duty to defend Daniels, American Guarantee lost its right to rely on these exclusions in litigation over its indemnity obligation.

It is quite clear that American Guarantee breached its duty to defend — indeed, it does not seem to contend otherwise now. We summarized the law applicable to this issue in Automobile Ins. Co. of Hartford v Cook (7 NY3d 131, 137 [2006]):

"It is well settled that an insurance company’s duty to defend is broader than its duty to indemnify. Indeed, the duty to defend is exceedingly broad and an insurer will be called upon to provide a defense whenever the allegations of the complaint suggest a reasonable possibility of coverage. If, liberally construed, the claim is within the embrace of the policy, the insurer must come forward to defend its insured no matter how groundless, [*4]false or baseless the suit may be.
"The duty remains even though facts outside the four corners of the pleadings indicate that the claim may be meritless or not covered . . . . Thus, an insurer may be required to defend under the contract even though it may not be required to pay once the litigation has run its course.""
 

"Here, the complaint in the underlying lawsuit against Daniels unmistakably pleads a claim for legal malpractice. American Guarantee no doubt had reason to be skeptical of the claim; it is unusual, in a loan transaction, for lenders to retain a principal of the borrower to act as their lawyer, as plaintiffs here claimed they did. But that means only that the claim against Daniels may have been "groundless, false or baseless . . . meritless or not covered" — it does not allow American Guarantee to escape its duty to defend. It would be different if the claim were collusive, but American Guarantee has neither claimed that plaintiffs and Daniels were colluding against it nor alleged any facts to support such a claim.

It is also well established that, when an insurer has breached its duty to defend and is called upon to indemnify its insured for a judgment entered against it, the insurer may not assert in its defense grounds that would have defeated the underlying claim against the insured (Lang v Hanover Ins. Co., 3 NY3d 350, 356 [2004]). As the court said in Mendoza v Schlossman (87 AD2d 606, 607 [2d Dept 1982]):

"A default judgment on the issue of liability in a legal malpractice action disposes of the issue of the lawyer’s negligence and the validity of the underlying claim."
The rule as we have just stated it does not dispose of the present case, because American Guarantee is not relying on defenses that would have shielded Daniels from malpractice liability; it is relying on exclusions in its insurance contract with Daniels. In Lang, however, we stated the rule more broadly:

"[A]n insurance company that disclaims in a situation where coverage may be arguable is well advised to seek a declaratory judgment concerning the duty to defend or indemnify the purported insured. If it disclaims and declines to defend in the underlying [*5]lawsuit without doing so, it takes the risk that the injured party will obtain a judgment against the purported insured and then seek payment . . . Under those circumstances, having chosen not to participate in the underlying lawsuit, the insurance carrier may litigate only the validity of its disclaimer and cannot challenge the liability or damages determination underlying the judgment."