The te-form is often thought of as the conjunctive form. This allows the combination of verbs, phrases, and sentences. The verb and/or phrase may even have a different meaning when it follows after the conjunctive.
The following are some uses. These are a sample of cases where the original verbial changes its meaning after it follows a te-form verb. You shouldn't restrict your usage of the te-form to these few uses.
- Explained in detail here.
When used as an auxiliary verb after the te-form, おく gives the sense of preparing a task or commiting to a task. It roughly translates to the English version of "I will do ...".
When used after the te-form, ある still has the same meaning as state-of-being, but it's more for the task being in a completed state. So, a person performed the te-form verb, and ある means the action is finished and remains in the finished state. There's no restriction for ある for inanimate and animate objects when following the te-form. This auxiliary verb is restricted to transitivity verbs only.