Clojure doesn't have date/time parsing in its "standard library" but there are several options out there. The most popular date/time library is clj-time which is a wrapper around Joda Time (a very popular Java library). Disclaimer: I am one of the current maintainers of clj-time, but it was a popular and mature library long before I got involved.
Add clj-time as a dependency in your project.clj (or build.boot) file, and then you'll need to require the coerce and format namespaces:
(require '[clj-time.coerce :as tc]
'[clj-time.format :as tf])
You'll need to create a "formatter" that matches the syntax of your date and time string when put together. The date part is straight forward (yyyy-MM-dd) but since you want to parse the AM/PM portion in your time part, you need to account for the 12-hour clock there (KK:mm aa):
(def my-date-time (str "2016-09-08" " " "3:45 PM"))
(def my-formatter (tf/formatter "yyyy-MM-dd KK:mm aa"))
Now you can parse your string to a Joda DateTime (in UTC) and then convert it to a Java Date to produce an instant literal in Clojure:
(tc/to-date (tf/parse my-formatter my-date-time))
;=> #inst "2016-09-08T15:45:00.000-00:00"
You can also do this directly via Java interop, using the Java standard library SimpleDateFormat and TimeZone classes:
(def sdf (java.text.SimpleDateFormat. "yyyy-MM-dd KK:mm aa"))
(.setTimeZone sdf (java.util.TimeZone/getTimeZone "UTC"))
(.parse sdf my-date-time)
;=> #inst "2016-09-08T15:45:00.000-00:00"
Using clj-time is generally going to produce much more idiomatic Clojure. For example, in the Java code above you have to create a mutable SimpleDateFormat object and then change its timezone to UTC via a method that returns void. Or rely on doto and Java interop like this:
(.parse (doto (java.text.SimpleDateFormat. "yyyy-MM-dd KK:mm aa")
(.setTimeZone (java.util.TimeZone/getTimeZone "UTC")))
my-date-time)
;=> #inst "2016-09-08T15:45:00.000-00:00"
In addition to parsing and formatting, the clj-time library provides conversions to/from several date/time-related types, as well as providing a rich library of date/time arithmetic and comparisons, with support for local date/time as well as UTC.