You can use pygame.key.get_pressed to do that.

Example:

while running:
    keys = pygame.key.get_pressed()  # Checking pressed keys
    if keys[pygame.K_UP]:
        y1 -= 1
    if keys[pygame.K_DOWN]:
        y1 += 1

The keyboard events (see pygame.event module) occur only once when the state of a key changes. The KEYDOWN event occurs once every time a key is pressed. KEYUP occurs once every time a key is released. Use the keyboard events for a single action or a step-by-step movement.

If you want to achieve a continuously movement, you have to use pygame.key.get_pressed(). pygame.key.get_pressed() returns a list with the state of each key. If a key is held down, the state for the key is True, otherwise False. It is a snapshot of the keys at that very moment The new state of the keys must be retrieved continuously in each frame. Use pygame.key.get_pressed() to evaluate the current state of a button and get continuous movement:

while running:
    for event in pygame.event.get():
         if event.type == pygame.QUIT:
             running = False

    keys = pygame.key.get_pressed()
    if keys[pygame.K_LEFT]:
        x1 -= 1
    if keys[pygame.K_RIGHT]:
        x1 += 1
    if keys[pygame.K_UP]:
        y1 -= 1
    if keys[pygame.K_DOWN]:
        y1 += 1

    setup_background()
    spriteimg = plumberright
    screen.blit(spriteimg, (x1, y1))

    pygame.display.flip()
    clock.tick(100)

See also Key and Keyboard event

Minimal example: repl.it/@Rabbid76/PyGame-ContinuousMovement

import pygame

pygame.init()
window = pygame.display.set_mode((300, 300))
clock = pygame.time.Clock()

rect = pygame.Rect(0, 0, 20, 20)
rect.center = window.get_rect().center
vel = 5

run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False
        if event.type == pygame.KEYDOWN:
            print(pygame.key.name(event.key))

    keys = pygame.key.get_pressed()
    
    rect.x += (keys[pygame.K_RIGHT] - keys[pygame.K_LEFT]) * vel
    rect.y += (keys[pygame.K_DOWN] - keys[pygame.K_UP]) * vel
        
    rect.centerx = rect.centerx % window.get_width()
    rect.centery = rect.centery % window.get_height()

    window.fill(0)
    pygame.draw.rect(window, (255, 0, 0), rect)
    pygame.display.flip()

pygame.quit()
exit()

Use this. It’ll work well. Put it in your for loop.

        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_a:
                playerX_change = -0.1
            if event.key == pygame.K_d:
                playerX_change = 0.1
        if event.type == pygame.KEYUP:
            if event.key == pygame.K_a or event.key == pygame.K_d:
                playerX_change = 0

    playerX += playerX_change
    player(playerX, playerY)
    pygame.display.update()

A simpler way can be:

KEYDOWN event to set a moving flag. KEYUP event to clear the flag.
For the movement process, just check the flag every frame. If set, move, and if unset then no move.

You can use KEYUP and KEYDOWN events.

You can continuously do your task while a key is down and when the key is up, just stop that task:

for event in pygame.event.get():
    if event.type == pygame.KEYUP:
        if event.key==K_DOWN:
            print("down key is not pressed")
    elif event.type == pygame.KEYDOWN:
        if event.key==K_DOWN:
            print('down key is not pressed now')

    pygame.event.clear() #optional only if your code requires
    # This will clear all events and the 'for' loop will be executed only once

I suggest to use the ‘clock’ function.

while running:
spriteimg = plumberright
screen.blit(spriteimg,(x1, y1))
spriteimg_x = 0
spriteimg_y = 0
spriteimg_speed = 0.2
dt = clock.tick(120)
    if event.type == pygame.KEYDOWN:
         if event.key == pygame.K_UP:
             x1 = x1 + 0
             spriteimg_y -= spriteimg_speed
         elif event.key == pygame.K_DOWN:
             x1 = x1 + 0
             spriteimg_y += spriteimg_speed
         elif event.key == pygame.K_LEFT:
             spriteimg_x -= spriteimg_speed
             y1 = y1 + 0
         elif event.key == pygame.K_RIGHT:
             spriteimg_y -= spriteimg_speed
             y1 = y1 + 0
    x1 += spriteimg_speed * dt
    y1 += spriteimg_speed * dt

How about this way? And… I thought the ticks’s value is so high…