I have recently started my fitness journey, and the trajectory is towards fat loss. Any tips?

My main tip is always to make the plan no more difficult than it absolutely needs to be in order to make progress.

Maybe you're already doing that, but a lot of people show up here thinking they need a lot of complicated, restrictive eating rules, and then they add punitively intense daily exercise. That's not sustainable, and it can even be counter-productive, for example by causing fatigue that bleeds calorie burn out of our daily routine because we drag through the day, rest more, etc.

I don't know what you mean by "eating clean", but by any definition I've ever seen, eating strictly clean is optional for weight loss. Yes, whole foods tend to be more nutrient dense and filling, which is helpful for weight management, but it needn't be a religion of perfection.

Strictly speaking, exercise is completely optional for weight loss. Yes, it's good for a body, and I recommend doing some of both cardiovascular and strength exercise in the long run. If you've previously been inactive, increase exercise gradually, trying to keep it manageably challenging, more energizing than exhausting. (A few minutes of "whew" right after the exercise is OK.)

Eat foods you like and find filling, in calorie-appropriate amounts. If you add exercise, try to find forms that you ideally find fun, worth doing for their own sake, but that at minimum are convenient, practical, and tolerable. In general, focus on how to make weight loss relatively easy, not how to make it happen fast. Make progress, don't worry about perfection.

IMO, the big goal, the golden prize, is not simply reaching goal weight, but staying at a healthy weight long term. (I say this from experience, now in year 8 of maintaining a healthy weight, after around 30 previous years of overweight/obesity.)

Reaching then staying at a healthy weight depends on finding new routine habits that can operate almost on autopilot when other parts of life get complicated, because - as you've learned - they will. "Find new, better permanent habits" is a very different mindset from "lose weight fast, then go back to normal".

I'll pick out that "comfort eating" point specifically. I don't know what's triggering the "comfort eating", i.e. whether stress, strong emotions, etc. Think about your triggers for comfort eating, at a time when you're not driven to do it, and identify some non-food (or non-calorie-laden) ways of comforting yourself.

I'd say: Sit down and make a list of some of those things. Put it somewhere you can look at it quickly next time you're tempted to comfort eat. Some things other people might list could include mild exercise (like a short walk), meditation/prayer, listening to soothing music, journaling, stretching/yoga, a creative pursuit (like sketching or playing a musical instrument), a warm shower or aromatherapy bubble bath, an absorbing hobby (like needlework, gardening, or carpentry), cuddling with a loved pet or child, etc. Even a low-calorie ritual like having some warm herb tea is fine.

If the trigger is emotion, some people make progress by simply sitting with and exploring that emotion. In general, if the underlying issue isn't fueling or nutrition, the best solution isn't food.

Only you know what could work for you. If you try something and it doesn't work, try something else. Be persistent. As long as you keep working at improving your plan, you'll eventually make progress.

I'll also say this: You mention some weeks going well, and others not. If the good weeks outweigh the bad ones, you'll still make progress. Strive for that: More good days than problem ones, more good days this week than last week, etc. If things go sideways, get back on your intended course as immediately as you can manage, none of this "start again Monday" or even "start again tomorrow". Start again NOW, if at all possible.

Ups and downs are human. Mastering our own ups and downs in ways that are realistic for us is empowering. That can build confidence. Learning the skill for chipping away at a big goal gradually, as is needful for weight loss, is a skillset we can then transfer to other areas of life: Career, education, finances, etc. Good stuff.

Best wishes for success!

P.S. You hash-tagged vegetarian. I'm vegetarian, have been for 50+ years. There are possibly some small nutritional complexities of weight loss specific to vegetarians, but generally vegetarianism is irrelevant to weight loss beyond that.