If I had to answer that in a few words, I would say "wait and watch". It is very natural to be concerned, but there is no need to act rashly and sell or even terminate your systematic investment plan (SIP). Here are a few guidelines to follow. Don't view any of them in isolation. But taken in conjunction, you would get a fairly good idea on what your next move should be or at least what you need to keep an eye on.
Check the fund's mandate
Some funds are very vulnerable to a fund manager's exit, others are not. If it is a fund that very closely tracks the benchmark (like an index fund) or has a very specific investment universe, then there should not be any cause for alarm. So funds that tap into the "top 100" or even "top 200" stocks by way of market capitalisation would not face too much of problem with a fund manager change. Neither would a fund that relies on a quant model for its stock picking process. Even the impact on a dividend yield fund would not be much.
If the fund is a multi-cap fund or a mid- and small-cap one, then the role of bottom-up stock picking and making the right calls is extremely important. A fund manager move in this case would be critical because it is his personal judgment that goes into adding alpha. So as you can see, not all fund managers are equally important to the funds they manage. Sometimes the very nature of the fund makes it less susceptible to fund manager changes. In other cases, it is cause for concern.
If it is a hybrid fund and the fund manager of the lesser allocated asset class leaves, then it should not bother you. For instance, if the fund in question is a 'Hybrid: Equity oriented' fund, then if the debt fund manager exits, it would not be as disquieting as in the case of the equity fund manager's exit. Also, in the case of fixed income there is not much of risk by way of credit and the fund's mandate generally states the maturity risk that is to be taken. Worst case scenario, you will get a mediocre performer but will be difficult to lose money.
Performance of other funds from the same stable
Look at the performance of the other equity schemes from the same fund house. Are there many which are also good performers? Or is it that all are poor performers and the only good one is the one you were holding? If you held the star performer and the fund manager has moved on, then it's cause for alarm.
Every asset management company (AMC) talks of processes being followed and how a fund manager exit would not affect any of the schemes. But that is not true. The fund manager's knowledge and expertise does make a difference. Unfortunately, end of the day, one does not really know how active a fund manager has been. But one way to gauge this is by looking at the performance of other funds from the same fund house. If a number of them are doing well, there could be a lot of truth to the 'processes' argument.
Fund manager's track record
There are two aspects to this.
First, look at the performance of other schemes run by the past fund manager. Did he have a positive impact on most of them? If he was lucky only with this one, it was probably the fund's mandate that worked in its favour.
Also, look at the performance of schemes managed by the new fund manager. What is his track record? If he has done a great job elsewhere, then he might just be a great fit for this fund, if not better. Consider that possibility too - that a new fund manager may actually work out better. If he has nothing to go by, or has been very average, then keep a very close watch on the fund.
Integrity of mandate
Talking of mandates, did the fund manager stick to his mandate? If it was a large-cap fund, were there times when his strategy changed to pack his portfolio with mid caps when the smaller stocks were rallying? If it was a thematic fund, did he follow the theme with precision? If not, then you should anyway ask yourself if you still want this fund in your portfolio.
Alternatively, if the fund manager did stick to his mandate, then you should keep a watchful eye to see if the new one at the helm is following suit. In other words - keep close track of the transition. He could maintain the same tilt of the fund, in terms of large cap, for instance, but might take a completely difference stance. If the earlier portfolio was largely into defensives, he may decide to get into momentum or growth stocks. Watch his moves, see how they perform and, most importantly, if they still are a good fit with your portfolio.