No, the existence of a CVE does not guarantee that a patch is available. A CVE may be published before a vendor has developed a fix, or even in cases where no fix is planned (for example, for obsolete or no longer maintained software). In these situations, users must implement workarounds or disable certain vulnerable features.
It is therefore essential not only to consult the CVE, but also to check the recommendations of the vendors and databases such as the NVD or the KEV database, which can indicate whether a patch exists and within what timeframe it is expected. Good risk management takes into account both the severity of the vulnerability and the availability of solutions.