There are some great answers here, and I hope my addition might also be of help. I spent the majority of my career in a hourly billable type role in tech consulting, so my advise may be a bit slanted by that.
(1) First and foremost, remember that as an employee you are essentially a small business of one and your employer is the customer of your services. In that mindset, since you can't grow your 'business' by hiring others and selling their services you must focus on how to improve yourself so that your skill and experience is worth more to your employer and thereby maximize your income from the limited number of hours you have to 'sell'. Always be on the lookout for opportunities to improve and expand your skills and to prove that you're ready for more responsibility. Recognize that problems your employer has are actually opportunities for you, whether as a lead or team player in solving them.
(2) You probably have an accurate understanding of your strengths and a fairly accurate understanding of most of your weaknesses, but the weaknesses that you're unaware of will hurt you the most - this is your blind spot. You must determine your hidden weaknesses and work to overcome them, and you're going to need the help from others to do this. If you meet resistance to growth in your career, rather than becoming discouraged seek advice and mentorship - you'll not only build a stronger network, but your mentors will definitely help identify your blind spot weaknesses and show you the path forward.
(3) Be flexible and easy to work with. This is true as an employee, and even more critical if you work directly with your employer's customers. As an old boss told me: When your customers have a need, you want them to think of you first because your competent and because they understand how to work with you and find it easy to do so. The reason everybody returns to the same grocery store every week is for similar reasons - because they know where the carts are, where the products are, and how to finish their shopping as quickly as possible.
(4) Be the expert. Your employer and customers are looking to solve problems; not to receive your opinion of how hard something is to do or what risks are involved. Those that lack confidence in their skills tend to focus on highlighting the risk of failure or hedge their bets in other ways. Those that have confidence don't necessarily ignore the risk, but do sell themselves as the expert qualified to tackle the job. If you want your employer to have confidence in you, you must have it in yourself. That said, don't 'damn the torpedoes' and scuttle your future.