If I implement Google Tag Manager (GTM) on my website, does that mean that I don't need to worry about Google Analytics (GA)?
GTM is not a replacement for Google Analytics (GA). It's a replacement for a small (but extremely important) piece of GA - the actual tracking code that sends data to GA.
So if you install GTM, you still need to place GA tags inside GTM and publish them if you want to collect valuable data.
GA is a reporting interface that can show you the results of the data you track online.
GTM helps you manage the tracking tags (pixels, scripts, code, etc.) that are used to track data. GTM also helps you connect the data you track across your marketing systems and analytics reporting interfaces.