So, if a SD tires of an SB and introduces her to his "friends". Is the Daddy a Pimp?

[Usual suspects]

And by "introduce to his friends," I mean teach her how to turn tricks one hour at a time.

Here is a copy of the Texas code:

Sec. 43.03. PROMOTION OF PROSTITUTION. (a) A person commits an offense if, acting other than as a prostitute receiving compensation for personally rendered prostitution services, he or she knowingly:
(1) receives money or other property pursuant to an agreement to participate in the proceeds of prostitution; or
(2) solicits another to engage in sexual conduct with another person for compensation.
(b) An offense under this section is a Class A misdemeanor, except that the offense is:
(1) a state jail felony if the actor has been previously convicted of an offense under this section; or
(2) a felony of the second degree if the actor engages in conduct described by Subsection (a)(1) or (2) involving a person younger than 18 years of age engaging in prostitution, regardless of whether the actor knows the age of the person at the time the actor commits the offense.

I just want to know if you can be prosecuted as a pimp without taking a cut of the cash?

[ShysterJon]

Yes, if you teach a girl how to be a hooker and find her johns, you're a pimp. You may want to supplement your wardrobe with a purple suit and a hat with a feather.

However, you probably won't be prosecuted under the scenario you present. LE doesn't care, you won't receive a cut of the proceeds, and there's no 'solicitation.'