Update September 18 2017: As of Insider Fast build 1710 (16.0.8530.1000), Advanced find is back on the Search Tools menu. This may be a temporary reprieve, until the new search tools are ready (which is how it should have been to begin with.) Note: Expanded Find Pane and More fields are still missing.
Users with the Insider builds noticed that Advanced Find is missing. This isn’t a bug; it was intentionally removed in preparation for improvements in search coming later this year. Based on data available to Microsoft (from people who agreed to share usage data with Microsoft), a very small percentage of users used Advanced Find. (Honestly, which is used more, Publisher or Advanced Find?)
While this is true, those who use Advanced Find rely heavily on it and it does one thing Instant Search can’t do: partial word searches. Plus, when Query Builder is enabled, users can easily create AND/OR queries.
Instant Search and Search folders can replace some of the functionality of Advanced Find (except for partial word searches). For better results, refine your Instant Search queries using logical operators AND, NOT, OR, <, >, =. For more information, see Instant Search Queries
You can voice your displeasure over this change in this Outlook Uservoice thread: Bring back Advanced Find to Outlook Search Tools.
Microsoft’s announcement: Upcoming changes for Recent Searches, Advanced Find, and Expanded Find