Thank you for asking this question. We are proud of you for prioritzing your healing while building new relationships.
Healing while building a new relationship requires self-awareness, patience, and open communication with your partner. To start,  honor your feelings. It is okay to slowly build trust and have the people in your life earn it. Be kind and patient with yourself.
Healing is an active process. To focus on it, prioritize things that encourage you to care for yourself, whether it's your physical, emotional, or mental wellbeing. Be your own scientist. Experiment with activities both alone and even with your new partner that make you feel grounded, capable, joyful, and safe. Also, make sure you are attending to your basic needs. This includes incorporating movement into your life, eating nourishing foods, and getting enough rest. Taking care of yourself will contribute to your overall healing and provide a solid foundation for your new relationship.
Breaking old habits of dependency or fear in a new relationship can be tricky. It can be a helpful starting point to reflect on the old habits that you want to break and try to understand triggers or patterns. You can do this through journaling, talking to a mental health provider, or talking to a trusted loved one. Take note of situations or behaviors that make you feel dependent or fearful in relationships. Also take note of situations that trigger you and create strategies to manage these triggers. Over time, you may decide to include your partner in some of these strategies to the extent that you both feel comfortable.
Next, open and honest communication with your partner is essential. Share your experiences and feelings at a pace that feels comfortable for you. Giving context for the fear you have within a relationship may give them more confidence to support you. Even a simple disclosure that "someone in the past harmed [you] causing [you] to want to take things slow" can help your new partner learn your needs and more about who you are. If your partner is not willing to respect your needs, that may be a sign that they might not be the appropriate person for you at this time. Although another person can't complete the healing process for you, they can certainly encourage and assure you along the way.
With this new relationship, move at a pace that feels comfortable for you. Listen to your intuition and communicate your needs and boundaries to your partner. This includes physical, emotional, and sexual boundaries (if you want to learn more about what to do if a partner pushes your boundaries in a way that makes you feel uncomfortable, read this FAQ). Allow trust to develop naturally as you get to know your partner better. Look for consistent behavior, empathy, and respect from them. Trust is built through actions and time.
Remember, you are WORTHY of love and respect. Sometimes you may not be your "best" self in your relationship, and that is okay. Breaking old habits takes time and effort, but it is possible. Be patient with yourself, be accountable for your actions when appropriate, and allow yourself to make mistakes. Surround yourself with supportive individuals who uplift and encourage you. You deserve a healthy and loving relationship external from your trauma.