Java 7, 138 106 105 bytes

String a(String a){return new java.text.SimpleDateFormat("HHmm").format(new java.util.Date("Ja1,0,"+a));}

Try it online!

Input is colon delimited and has a space between the time and the am/pm. Output is not colon delimited.

Java 7, 138 106 105 104 bytes

String a(String a){return new java.text.SimpleDateFormat("Hmm").format(new java.util.Date("Ja1,0,"+a));}

Try it online!

Input is colon delimited and has a space between the time and the am/pm. Output is not colon delimited.

-1 byte thanks to Kevin Cruijssen

Java 7, 138 106 bytes

String a(String a){return new java.text.SimpleDateFormat("HHmm").format(new java.util.Date("Jan1,0,"+a));}

Try it online!

Input is colon delimited and has a space between the time and the am/pm. Output is not colon delimited.

Java 7, 138 106 105 bytes

String a(String a){return new java.text.SimpleDateFormat("HHmm").format(new java.util.Date("Ja1,0,"+a));}

Try it online!

Input is colon delimited and has a space between the time and the am/pm. Output is not colon delimited.

Java 7, 138 bytes

import java.text.*;String a(String a)throws Exception{return new SimpleDateFormat("HHmm").format(new SimpleDateFormat("hhmma").parse(a));}

I know this is the most naive approach and you can probably do it shorter with clever string manipulation but this is the first thing that came to mind. Input is not colon delimited and has no space between the time and the am/pm. Output is not colon delimited.

Java 7, 138 106 bytes

String a(String a){return new java.text.SimpleDateFormat("HHmm").format(new java.util.Date("Jan1,0,"+a));}

Try it online!

Input is colon delimited and has a space between the time and the am/pm. Output is not colon delimited.