Your question is exactly the question that is answered by reading Domain-Driven Design.

The comment from Andy is spot-on. The entities don’t depend on DAOs. They depend on abstractions that represent operations the entities need to function. The fact those abstractions represent data storage and are implemented using database is irrelevant to entities or any part of domain model. Those abstractions are called Repository in DDD.

To answer your questions:

• How services are initialized and injected into domain entities? – When entity is pulled from persistence, it is initialized with realizations of abstractions it needs, alongside the data of the entity.
• What about single responsibility paradigm? – What about it? The entity has only one responsibility : represent behavior related to single domain concept.
• And isn’t it against reusablity? – It is actually highly reusable. Especially if you apply other SOLID principles and use composition instead of inheritance.

For your example, that can be easily solved by Agent having reference to interface, that allows it to query cards in different way. The methods then call this interface.

What do you mean by But then Agent shall depend on 3 DAO classes for just one responsibility? If you’re talking about avoiding DAO call from domain classes, maybe you can design it like this:

class Agent {

   List<Card> assignedCards;

   int numberOfRemainingCards() {
      return assignedCards.size();
   }

   void sell(Card card) {
      // do something
      assignedCards.remove(card);
   }

   void damaged(Card card) {
      card.damaged = true;
      assignedCards.remove(card);
   }

}

class Card {

   String id;

   boolean damaged;

}

You only need one call to DAO (or repository) to retrieve an Agent with their assignedCards. It only involves one DAO, for example:

List<Agent> agents = AgentDAO.getAllAgents();
for (Agent agent: agents) {
   System.out.println("Remaining cards for " + agent.name + 
                      " is " + agent.numberOfRemainingCards());
}

Another example:

Agent agentA = AgentDAO.findByName("Agent A");
agentA.sell(aCard);
agentA.damaged(anotherCard);
System.out.println("Number of remaining cards: " + agentA.numberOfRemainingCards());
AgentDAO.update(agentA); // if necessary

If Agent has a lot of Card and you don’t want to retrieve all Card just for determining number of remaining Cards, you can store the number of remaining cards as state, for example:

class Agent {

   List<Card> assignedCards;

   int numberOfRemainingCards;

   int getNumberOfRemainingCards() {
      return this.numberOfRemainingCards;
   }

   void sell(Card card) {
      // do something
      assignedCards.remove(card);
      numberOfRemainingCards--;
   }

   void damaged(Card card) {
      card.damaged = true;
      assignedCards.remove(card);
      numberOfRemainingCards--;
   }

   void assign(Card card) {
      assignedCards.add(card);
      numberOfRemainingCards++;
   }

}