I am going to try to answer this honestly, which means acknowledging upfront that I have an obvious interest in the answer. Take that into account. Then consider that the consulting engagements that go badly, for both the client and the consultant, are almost always the ones where the wrong tool was applied to the problem.
So here is a genuine attempt at a useful answer.
When a consultant is the right call
When you need a capability you do not have and do not need to build.
Some problems require skills or experience that your organisation does not have and will not need on an ongoing basis. A major technology selection happens once every five to ten years. A merger integration might happen once. A market entry strategy for a new geography might be a one-time exercise. Hiring a permanent resource for work like this is rarely the right answer. Bringing in someone who has done it many times before, and will hand over cleanly when it is done, often is.
When you need an outside view.
Organisations get used to their own blind spots. The way things have always been done becomes invisible. The assumptions that underpin the strategy stop being examined. An outside perspective, applied by someone who has seen a range of different organisations operate, surfaces things that internal teams often cannot see because they are too close to them.
This is not about intelligence. Smart, experienced internal teams develop blind spots. It is structural.
When the work needs to happen faster than your internal capacity allows.
The leadership team has a strategy it needs to execute but no spare capacity to run it. The operational team is at full stretch with the day job. There is a program that needs dedicated resource for twelve months, and hiring permanent people for work that will not exist after that does not make sense. A consultant fills that gap without the ongoing commitment.
When independence matters.
Sometimes the outcome needs to be credible to an audience that would discount an internal recommendation. A board reviewing a major strategic decision, an acquirer assessing a business, a regulator examining a compliance program. An independent assessment from someone with no stake in the answer carries weight that an internal recommendation sometimes cannot.
When a consultant is probably not the right call
When the problem is actually a leadership or culture issue.
Consultants can help design solutions. They cannot implement culture change on your behalf. If the real problem is that the leadership team does not agree on direction, or that there is a trust problem between functions, or that a specific leader is not performing, bringing in external help to work around those issues tends to delay the real conversation rather than resolve it.
When you do not have the internal capacity to absorb the work.
A consultant can produce a strategy, a plan or a design. But the organisation has to implement it. If the business does not have the leadership attention, the internal capability, or the change capacity to do something with the output, the engagement will produce a document rather than a result. The question to ask before bringing in help is not just "what do we need?" but "are we ready to act on it?"
When you are not sure what the problem is and are hoping a consultant will work it out.
Consultants are good at solving problems. They are less useful as a substitute for the internal clarity that should come first. The best engagements start with a leadership team that has a clear view of the problem they are trying to solve, even if they do not know how to solve it. If the brief is vague, the output tends to be too.
How to tell before you sign anything
A few things worth doing before committing to an engagement.
Have an honest conversation about what you are trying to achieve and what success looks like. If the consultant cannot articulate that back to you clearly, or is not asking the right questions to understand it, that is useful information.
Ask for examples of similar work and talk to the people who were on the receiving end of it. Not the references the consultant volunteers, the ones you ask for.
Make sure the commercial model reflects the scope. Fixed price for well-defined work. Time and materials for discovery and complex programs. Be cautious about open-ended arrangements without clear milestones.
And if something in the scoping conversation does not feel right, say so. The quality of the relationship in the scoping phase tends to predict the quality of the engagement itself.