Paying attention to the time is an important skill to develop for many reasons. In the absence of a submission, we have a limited amount of time to establish something significant. Different time frames have different strategies and levels of effort. This is my general approach.
The amount of time we train impacts how much effort can be exerted without fear of trying too hard. If we overextend our resources, we will be too tired to move correctly for the remaining time. People use the clock in every sport that keeps track, but there are a few quirks in Bjj.

Early in the round.
The first to score points is the most likely to win. This is true in Bjj as much as any other game. We want to be ahead on points as soon as possible. A submission in a gym roll is only an invitation for our training partner to start from the beginning again. This is another reason why a strong opening game is important. You will want:
1: A simple plan from standing. Take down who you can, it’s the shortest path to two points. Don’t dance for longer than a minute unless you have eight or more minutes to work.

2. An immediate threat from guard. Never pull guard out of fear. Instead, go into an immediate sweep/submission threat. A sweep will put you ahead on points first. If you can secure a quick submission, you will be fresh for later rounds in big tournaments.
3. A conservative guard pass. If they pull first, you can take more time pressure passing. Moving too much gives openings that could get you swept or submitted. We aren’t allowed to avoid engaging the guard. That would be silly anyway.

The middle game.
After two minutes, we have a good feel for the problem we are solving here. An early submission was a no go, and someone usually has either points or at least established top position. In gym rolls, this is when upper belts will often impose involuntary drilling. Instead of restarting over and over from the beginning, they keep you in a study of their choice. You’re going to burn up the time somewhere, and this is it.
By the book, we follow the natural progression. Establish top position, pass the guard, mount and submit. We need to hold each position for at least three seconds before getting our points. You will see experienced competitors holding knee on belly and looking at the referee to ensure they got their points. Many people experience time distortion in a match, so looking up at the clock is a good habit.
Two middle game situations.
If we are ahead on points, it can be tempting to stall. After 20 seconds of deliberate inaction, we get called for stalling. (Mount and Back are the only exceptions.) This leaves us with plenty of time to make an attempt to progress or submit them. There is no reason to move backwards to score points again. In gym rolls, you can let people regain their guards and practice stopping the reguard at various stages. Deliberately spending time passing in gym rolls allows people to develop their games and recognize patterns that get them passed. As we get closer to the bigger competitions, it’s a good idea to start deliberately holding mount and back for longer periods of time. Someone who has been mounted for one minute behaves totally different from someone who just got mounted.
If we are behind on points, carefully open up a little bit. On top, change directions more often to create openings more aggressively. On bottom, take gradually bigger risks to try to get a guard back. If a guard is established, we can focus on finding a way to off balance them. There is still time to work, but give yourself a set amount of time to test instead of overcommitting to a failing plan. Think one or two minutes at closed guard, then try a strong open guard if nothing happens.
The last minute.

We are decisively either winning or losing at this point. This is why short rounds tend to be more intense.
If we are winning, they are more likely to make dramatic movements. It can be either the perfect moment to attack a submission, or a bait to get us to make a mistake.

If we are losing, this is our last chance to make something happen. Amazing comebacks are cool, but we messed up by letting it go this far. Don’t blow anything out trying to make up for a mistake. Learn from the experience and try again!