Why do we bother having councillors? To make all of the decisions. Why do we bother having clerks? To act upon those decisions and all other legitimate instructions issued by the council.
If your clerk is not performing the role agreed by the council, the council must act, however difficult that may be. Does the clerk have a contract of employment including a job description for the role? Has the council adopted model grievance and disciplinary policies? If the answer to both of the above is yes, your staffing committee, if you have one, or a duly authorised small group of councillors (but not an individual), must meet with the clerk to explain the council's concerns and clarify the cause of the delays. There may be valid reasons that you will need to take on board as a responsible employer. Aim to set a reasonable list of targets for each of the key tasks and agree how these will be monitored. It is absolutely vital that you follow your own policies and procedures to the letter in addressing this situation, as that will be the subject of any employment tribunal.
If you haven't adopted the model documents, you don't need an HR consultant. They're available on the NALC website (members' section) so you can download them, fill in the blanks and approve them at your next meeting. A word of caution about the use of consultants. The world of local government is a mysterious place unlike anything you will find in the real world, so a consultant without significant local government experience might land you in a whole heap of bother.