Jewish law has long recognized the advantages of a competitive marketplace and thus places few restrictions on entrepreneurs. Thus one may open a pizza shop next door to a pre-existing one or set up a law office down the hall from your competition. While some authorities limit freedom of entry to situations where the market is large enough to support multiple businesses, many authorities allow for competition even when the market is such that one (or both) of the firms is destined to go out of business. Thus in a large metropolitan area all are welcome to open competing businesses.
Nonetheless employees who leave their firm to strike out on their own - a fairly common occurrence - must ensure they do not run afoul of several moral exhortations. While you may welcome former clients who seek out your "new" services" one would be enjoined from any attempts at soliciting their business, notwithstanding the fact that you may have been solely responsible for the account for many years. These clients belong to the firm and attempting to lure them away would run afoul of the prohibition of exploiting the efforts and or assets of others for personal gain. A fine line but one that may not be crossed. Similarly any unique "trade secrets" developed by the former firm may not be used in ones new employ. Furthermore one may not take along key employees with him. To do so is not considered fair competition but rather directly raiding and damaging the competition something which Jewish law prohibits. Thus enlisting a head hunter to attempt to lure the key players in, for example, a rivals legal department would appear to be prohibited.
The Talmud labels one who "snatches away the anticipated gains of others" a rasha , an evil person. Many Rabbinic authorities, in applying this dictum to the modern workplace prohibit the stealing of longstanding clients of rival firms. This of course applies to all competitors not just former employees and would proscribe unsolicited bids for clients, even if such bids were to offer cost savings. Rather one may do generic advertising hoping that some may recognize your talents and voluntarily choose your services.