Bash prompt can be set by setting the environment variable PS1. We need to update this variable to get time in our prompt.

There are 4 ways to get the time in prompt. If you see manual page for bash, you can see time can be set using:

\t     the current time in 24-hour HH:MM:SS format
\T     the current time in 12-hour HH:MM:SS format
\@     the current time in 12-hour am/pm format
\A     the current time in 24-hour HH:MM format

Note that the time is not the current time but the time when prompt was last updated. Prompt will be updated when previous command completed.

Sample usage:

PS1="\t $ "   # 11:13:54 $ 
PS1="\T $ "   # 11:14:01 $ 
PS1="\@ $ "   # 11:14 AM $ 
PS1="\A $ "   # 11:14 $ 

Add whichever style you like to your $HOME/.bashrc and every time you open a new terminal, you will see time in command prompt.

If you wish to show current directory with time in prompt, a nice prompt setting could be like

PS1="\w \A $ "
PROMPT_DIRTRIM=2
# Resulting in prompt to look like
# ~/.../bluetooth/nimble 11:16 $ 

Here PROMPT_DIRTRIM would set the number of parent directories you wish to see in the prompt.

Checkout designing a minimal bash prompt.