Yes. The compensation for the miners comes in the fees within the blocks. I'm assuming that the volume of transactions by then or the derived fee as a result of off-chain transactions would be sufficient to compensate for it.
It is highly unlikely that Bitcoin would insecure by then. The way the block rewards are reduced gradually pads any impact on the miner's income and we're most likely going to see the impact far sooner than the 2140 timeline.
When you talk about the fees for off-chain transactions, are you thinking about exchanges dividing their profits with miners? Or what other off-chain transactions are there that generate a fee?
For now we still have enough time to figure out a way to make Bitcoin work even when there are no coinbase transactions anymore. But that is still some time to go.