You'll sometimes hear that a 1031 exchange 'resets' depreciation on the replacement property. That's an oversimplification, and acting on it can produce an unpleasant surprise at tax time.
In an exchange, basis generally carries over with adjustments. Depreciation treatment after an exchange is more nuanced than starting fresh, and the deferred gain embedded in the carryover basis doesn't disappear. Additional investment above the relinquished property's value may be treated differently than the carryover portion.
Depreciation also matters on the way out. Depreciation claimed or allowable over decades of ownership reduces adjusted basis, which increases realized gain on a taxable sale, and a portion may be subject to unrecaptured Section 1250 treatment at a different rate than long-term capital gain.
The practical takeaway: ask your CPA to model both the taxable-sale scenario and the exchange scenario using your actual depreciation schedule before you decide anything.