So you’ve just started a new job, you know what needs to be changed but you have no resource to implement the required change. The only route is to use outside resource - maybe use consultants! But you are concerned that this action will be seen as a sign of weakness and be criticised by your boss and subordinates so you do nothing.
This is a common dilemma but the action described is incorrect. You have used your expertise to identify the problem, not only that you’ve identified what is stopping you getting rid of the problem - what’s constraining the desired change. The correct action is to use outside resource ensuring it has a good brief - and maybe paid by results. Yes it will cost money but this will be far out weighed by your Company’s performance improvement. Not only that the cost of outside resource stops as soon as the brief is fulfilled.
Now not improving your Company performance when you know how to do it is a criticism!