"Undue delay" refers to waiting longer than necessary or reasonable. It suggests that an action or process is taking too much time or being unnecessarily delayed, which may cause problems or inconvenience. Full definition
A lawyer should not undertake a matter without honestly feeling competent to handle it, or being able to become competent without undue delay, risk, or expense to the client. (slaw.ca)
For this reason I conclude that only the delay from commencement of the action is appropriate for purposes of considering whether there has been undue delay in the progress of the litigation. (slaw.ca)
On that basis a duty to avoid undue delay would be owed to all, effectively creating «back door» liability for breach of statutory duty. (newlawjournal.co.uk)